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1/3p+7=3/4p+9
We move all terms to the left:
1/3p+7-(3/4p+9)=0
Domain of the equation: 3p!=0
p!=0/3
p!=0
p∈R
Domain of the equation: 4p+9)!=0We get rid of parentheses
p∈R
1/3p-3/4p-9+7=0
We calculate fractions
4p/12p^2+(-9p)/12p^2-9+7=0
We add all the numbers together, and all the variables
4p/12p^2+(-9p)/12p^2-2=0
We multiply all the terms by the denominator
4p+(-9p)-2*12p^2=0
Wy multiply elements
-24p^2+4p+(-9p)=0
We get rid of parentheses
-24p^2+4p-9p=0
We add all the numbers together, and all the variables
-24p^2-5p=0
a = -24; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-24)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{25}=5$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-24}=\frac{0}{-48} =0 $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-24}=\frac{10}{-48} =-5/24 $
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